graph the function $f(x) = 2x^2 + 4x + 5$.

plot the vertex. then plot another point on the parabola. if you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Question

graph the function $f(x) = 2x^2 + 4x + 5$.

plot the vertex. then plot another point on the parabola. if you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Quadratic Vertex", "Finding Parabola Points" ], "new_concepts": [], "current_concepts": [ "Quadratic Vertex", "Finding Parabola Points", "Graphing Quadratic Functions" ] } ## Find the vertex of the parabola $$ \begin{aligned} &a = 2,\quad b = 4,\quad c = 5\ &x_v = -\frac{b}{2a} = -\frac{4}{2(2)} = -1\ &y_v = f(-1) = 2(-1)^2 + 4(-1) + 5 = 2 - 4 + 5 = 3\ &\text{Vertex: } (-1, 3) \end{aligned} $$ ## Find another point on the parabola $$ \begin{aligned} &x = 0\ &f(0) = 2(0)^2 + 4(0) + 5 = 5\ &\text{Point: } (0, 5) \end{aligned} $$ To graph the function $f(x) = 2x^2 + 4x + 5$: 1. **Vertex**: $(-1, 3)$ 2. **Another point**: $(0, 5)$ { "elements": [ { "type": "point", "params": [[-1, 3]], "properties": { "name": "Vertex (-1, 3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0, 5]], "properties": { "name": "Point (0, 5)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "2*x*x + 4*x + 5", "latex": "2x^2 + 4x + 5"}, -10, 10], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Quadratic Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Find the vertex of the parabola

Find another point on the parabola

Answer: